Had this happen on the 2200 a couple of weeks ago. If the face plate looks good check for friction on the rear brake cable or a slightly binding rear brake. The rear brake spring does a lot to pull the brake level tight against the body. The right fix for me should have been to tear the brake apart, clean and lube it but the quick fix was to flush out the gunk by shooting a little (bike gods forgive me) WD-40 on the rear brake pivot points. Let us know what you find.
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'89 Trek 1200 ,'89 Trek 400 , '97 Trek 720 , '99 Trek 2200, '02 Trek 520.